Chaotic attitude oscillations of a satellite filled with a rotating ellipsoidal mass of liquid subject to gravity-gradient torques

The Hamiltonian equations of a liquid-filled satellite subject to gravity-gradient torques in terms of the generalized Deprit variables are established for applying the Melnikov theory formally. The heteroclinic orbits of the torque-free symmetric liquid-filled satellite are found. A criterion for the heteroclinic transversal intersections at the onset of chaotic attitude is formulated using Melnikov's integral. The results from the Melnikov theory are crosschecked with simulation.     

Analysis and numerical solution of a functional differential equation

In the present work we investigate the existence, uniqueness and computation of the solutions of an initial value problem for a class of functional differential equations involving autoregulations in the limits of the integration.     

Variable Programming: A Generalized Minimax Problem. Part II: Algorithms

In this part of the two-part series of papers, algorithms for solving some variable programming (VP) problems proposed in Part I are investigated. It is demonstrated that the non-differentiability and the discontinuity of the maximum objective function, as well as the summation objective function in the VP problems constitute difficulty in finding their solutions. Based on the principle of statistical mechanics, we derive smooth functions to approximate these non-smooth objective functions with specific activated feasible sets. By transforming the minimax problem and the corresponding variable programming problems into their smooth versions we can solve the resulting problems by some efficient algorithms for smooth functions. Relevant theoretical underpinnings about the smoothing techniques are established. The algorithms, in which the minimization of the smooth functions is carried out by the standard quasi-Newton method with BFGS formula, are tested on some standard minimax and variable programming problems. The numerical results show that the smoothing techniques yield accurate optimal solutions and that the algorithms proposed are feasible and efficient.This work was supported by the RGC grant CUHK 152/96H of the Hong Kong Research Grant Council.     

Chaotic rotations of a liquid-filled solid

The disturbed Hamiltonian equations of a solid filled with a rotating ellipsoidal mass of a liquid and subjected to small-applied moments are revisited using Deprit's variables. We investigate the chaotic dynamics of the orbiting liquid-filled solid and of the liquid-filled solid sliding and rolling on a perfectly smooth plane, in either energy-conservative or energy-dissipative conditions, when appropriately perturbed. Criteria for the judgment of potential chaotic rotations of the perturbed system are formulated by means of Melnikov-Holmes-Marsden (MHM) integrals. Strategies for the solution of heteroclinic orbits of the symmetrical liquid-filled solid under torque-free conditions are outlined theoretically. Physical parameters that will probably trigger the onset of chaotic motions can be determined accordingly. Results from MHM algorithms are crosschecked with Poincare sections together with Lyapunov characteristic exponents.     

Large negative Goos-Hanchen shift at metal surfaces

It has been previously established that for p-polarized light incident onto a semi-infinite absorbing medium, large negative Goos-Hanchen (GH) shifts can be expected in the case of weak absorption at incidence close to the Brewster angle. The effect has been demonstrated for certain semiconducting media at optical frequencies. Here we point out that similar phenomenon can take place for strongly reflecting and attenuating medium such as metal at IR frequencies, with large incident angles close to grazing incidence. Moreover, unlike the previously-studied case with semiconductors, the Brewster angle in the present case with metals plays an insignificant role in the possible hindrance of the observation of such large negative shifts.     

Synthesis and structural characterization of 5,6,15,16-tetradehydrobenzo[a]phenanthro[9, 10-e]cyclooctene,C24H12

A benzo-phenanthro-fused planar cyclooctatetraene derivative, namely, 5,6,15,16-tetradehydrobenzo[a]phenanthro[9, 10-e]cyclooctene (5) was synthesized in two steps from the known benzo[a]phenanthro[9, 10-e]cyclooctene (6). Compound5 crystallizes in space groupPbam witha=9.828(2),b=19.466(4),c=15.901(3) Å, and Z=8. X-Ray analysis (MoK radiation,R=0.060 for 1233 observed data) has shown that both independent molecules have the same planarC _2v configuration with averaged bond lengths of 1.381(7) and 1.208(7) Å for the phenanthrene C_6a–C_14b bond and the acetylenic CC bond, respectively.¹H and¹³C NMR spectral results of 5 and 5,6,15,16-tetrabromo-5,6,15,16-tetrahydrobenzo[a]phenanthro[9, 10-e]cyclooctene (7) are also presented.     

Homogentisic acid γ-lactone suppresses the virulence factors of Pseudomonas aeruginosa by quenching its quorum sensing signal molecules

Homogentisic acid γ-lactone exhibited excellent anti-quorum sensing (QS) and anti-biofilm activities against Pseudomonas aeruginosa. Moreover, it suppressed the QS-dependent virulence factors in P. aeruginosa by quenching its QS signal molecules.     

Total Synthesis and Conformational Study of Callyaerin A: Anti‐Tubercular Cyclic Peptide Bearing a Rare Rigidifying (Z)‐2,3‐ Diaminoacrylamide Moiety

The first synthesis of the anti‐TB cyclic peptide callyaerin A ( 1 ), containing a rare (Z)‐2,3‐diaminoacrylamide bridging motif, is reported. Fmoc‐formylglycine‐diethylacetal was used as a masked equivalent of formylglycine in the synthesis of the linear precursor to 1 . Intramolecular cyclization between the formylglycine residue and the N‐terminal amine in the linear peptide precursor afforded the macrocyclic natural product 1 . Synthetic 1 possessed potent anti‐TB activity (MIC₁₀₀=32 μm ) while its all‐amide congener was inactive. Variable‐temperature NMR studies of both the natural product and its all‐amide analogue revealed the extraordinary rigidity imposed by this diaminoacrylamide unit on peptide conformation. The work reported herein pinpoints the intrinsic role that the (Z)‐2,3‐diaminoacrylamide moiety confers on peptide bioactivity.